The present invention relates in a broad aspect to a method for design and modification of airfoils useful for wind turbine applications, which airfoils possess smooth and stable characteristics in stall. These characteristics comprise: (1) No or very little tendency to double stall, (2) Insensitivity or little sensitivity of maximum lift to leading edge roughness, (3) High lift-drag ratio just before maximumlift, (4) Small variations of the aerodynamic loads in stall and (5) Sufficient aerodynamic damping to suppress blade vibrations in stall. The invention further relates to blades and/or airfoil sections in general which posses smooth and stabile characteristics in stall. Also, it relates to a method of implementing the desired shape on an airfoil or a wind turbine blade.
An increasing problem at least within the wind turbine industry is poor power quality, high fatigue loads and unreliability of power and loads for wind turbines operating at high wind speeds where the airfoil sections or blades are just before or in stall.
The airfoil sections on the blades operate at angles of attack ranging from low angles of attack, where the lift is low on the linear part of the lift versus angle of attack curve, to high angles of attack where the airfoil section is just before stall or in stall. This is in contrast to other traditional aviation applications such as aeroplanes and helicopters. Especially operation in stall is unique for some wind turbines, which use stall as a way of controlling the peak power which is also called the rated power.
The following parameters influence the operation in stall:
Double stall denotes the situation wherein the flow past an airfoil section or blade having an angle of attack relative to the free stream flow shows at least two levels of lift and drag to the same angle of attack.
The problem becomes even larger when a wind turbine is operating in stall regulated mode, i.e. the power of the turbine is limited by stall on the blades and the lift and drag produced by the blade or airfoil section may jump between at least two levels showing at least two levels in generated power and/or thrust on the rotor. When the power jumps from on level to another the aerodynamic forces acting on the blade or airfoil section dramatically changes. This may cause uncertainties of the power level and thereby uncertainties in the prediction of the energy production. Furthermore, large vibrations induced in the turbine may be the result which at the end may cause break down of the turbine.
Leading edge roughness around maximum lift both at stall and in stall can appear when the leading edge part of the airfoil section or blade is accumulating bugs, dust, ice or other kind of material changing the roughness of the existing airfoil section or blade and the effective flow pattern around the airfoil section or blade.
Leading edge roughness around maximum lift both just before stall and in stall is often observed on wind turbines. It causes uncertainties of the power level and thereby uncertainties in the prediction of the energy production. Furthermore, the loads on the structure will change, which might result in undesirable structural dynamics.
The lift-drag ratio is a measure of the efficiency of the airfoil section or blade. The higher ratio the better efficiency. Thus, the lift-drag ratio can be improved by increasing the lift and/or decreasing the drag.
It is desirable that the lift-drag ratio just before stall is high. This is because maximum power of the wind turbine this way will be obtained at lower wind speeds and the annual energy production will increase.
The variation of the aerodynamic loads can be measured as the standard deviation of the aerodynamic lift and drag. A high standard deviation of lift and drag means that the variation of the aerodynamic loads is high. Especially in stall the standard deviation can be high, indicating that the flow is not smooth and stable.
When operating in stall it is important that the variation of the aerodynamic loads is as small as possible. This is because the structure will respond on the aerodynamic loads. Thus, large variations in the loads will cause vibrations in the structure resulting in higher fatigue loads and more noise. Furthermore, the quality of the produced power may become poorer with larger variation in the aerodynamic loads. Very big variations in the loads are observed when double stall appears.
The total damping of a wind turbine blade is the sum of the structural damping and the aerodynamic damping. Aerodynamic damping is a measure for how well the blade structure is damped when influenced by aerodynamic loads. Especially when operating under stalled conditions there is a risk for negative total damping. If the positive structural damping is less than the negative aerodynamic damping severe vibrations of the structure will appear possibly resulting in break down of the structure.
For wind turbines operating in high wind speeds vibrations of the blades both in the rotor plane and out of the rotor plane can occur. This is a very undesirable situation and can be avoided by changing the stall characteristics of the airfoils used for the blades.
Therefore a technical problem in connection with the above mentioned parameters influencing stall is to provide airfoil sections or blades wherein the risk of presence of double stall, significant influence of leading edge roughness, low lift-drag ratio just before stall and in stall, big variations of the aerodynamic loads and/or negative aerodynamic damping is minimised and in some cases avoided.
As many turbines today are utilising airfoil sections or blades producing double stall, big influence of leading edge roughness, low lift-drag ratio just before stall and in stall, big variations of the aerodynamic loads and/or negative aerodynamic damping a further problem is to modify these turbines, that is modify the blades of existing wind turbines or modify the existing moulds for airfoils and/or blades.
These problems have been solved by means of the present invention, which provides two- or three-dimensional cross sectional airfoil data, such as airfoil sections or blades, useful for aerodynamic applications such as for a wind turbine, wherein the airfoil section contour or parts thereof or wherein the contour of the blade or parts thereof have been modified to avoid one or more of the problems listed below:
Generation of double stall, that is the flow past the airfoil section or blade shows at least two different lift and/or drag levels to the same angle of attack. According to several aspects of the present invention, aerodynamic airfoil sections or blades are designed which when exposed to a stream of fluid they do not have the tendency of generating a burst of a leading edge separation bubble as such a leading edge separation may be the source of double stall phenomena.
Sensitivity to leading edge roughness, that is where the airfoil shows a decrease in the lift and an increase in the drag just before stall and in stalled conditions when bugs, dust, ice or other pollutants accumulate at the leading edge part of the airfoil. According to several aspects of the present invention, aerodynamic airfoil sections or blades are designed which when exposed to a stream of fluid they show less sensitivity to leading edge roughness in stalled conditions.
Low lift-drag ratio at angles of attacks just before maximum lift, that is where the airfoil section or blade just before maximum lift shows a certain efficiency. According to several aspects of the present invention, aerodynamic airfoil sections or blades are designed which when exposed to a stream of fluid they show an increased lift-drag ratio at angles of attacks from just before maximum stall and until lift and thereby an increased efficiency in this angle of attack interval.
Big variations in the aerodynamic loads, that is where the airfoil in stalled conditions shows a certain standard deviation in lift and/or drag. According to several aspects of the present invention, aerodynamic airfoil sections or blades are designed which when exposed to a stream of fluid they show a decreased standard deviation of lift and/or drag in stalled condition.
Negative aerodynamic damping, that is where the airfoil in stalled conditions shows a certain negative aerodynamic damping. According to several aspects of the present invention, aerodynamic airfoil sections or blades are designed which when exposed to a stream of fluid they show an increase in the aerodynamic damping in stalled conditions.
These designs are in a general aspect of the present invention aimed at modifying existing airfoil sections or blades applied in wind turbine applications as many existing wind turbines suffers the problems of poor power quality, high fatigue loads, aerodynamically induced vibrations and/or unreliability of power and loads for wind turbines operating at high wind speeds where the airfoil sections or blades are just before or in stall which is believed to be associated with the problems listed above.
Some attempts have been put forward in the past which in generally have led to devices for disturbing the airflow boundary layer on the airfoil section or blade so much that the boundary layer flow undergoes transition from laminar to turbulent flow in an abrupt way in order to stabilise the flow. None of these devices have had an aerodynamic shape so that the surface and/or the tangent to the surface in the vicinity of the intersections between the device and the airfoil and blade are smooth such as continuous. These devices are characterised in being flat plates extending normal to the surface of the airfoil section or blade, which is only naturally as the understanding of the flow associated with the problems listed above has not been accomplished earlier. Accordingly, none of these devices have been designed with the objective to avoid double stall, to improve the insensitivity to leading edge roughness in stalled conditions, to increase the lift-drag ratio just before stall and in stalled conditions and/or to decrease the variations of the aerodynamic loads in stall whereby the design of these devices has led to devices producing for instance very high drag.
On the other hand, recent research has revealed some perception of the phenomena termed double stall as disclosed in C. Bak, H. A. Madsen, P. Fuglsang, F. Rasmussen; xe2x80x9cDouble Stallxe2x80x9d; June 1998 (1998-06); Riso National Laboratory, Roskilde; XP002140078. This document discloses calculations and wind tunnel tests of flows past different airfoil sections at different conditions and concludes that there could be a connection between the position of a real upper side free transition point being close to a real critic transition point (that is the transition point which trick bursting of a leading edge separation bubble) and double stall. However, no conclusion is disclosed and in particular neither modifications to airfoils nor methods for designing airfoils are disclosed.
Also, the patent application PCT/US98/24952 by Midwest Research Institute describes airfoils for wind turbines. However, this description does not contain a description of modifications of existing airfoils and/or blades. Neither does it describes a design method nor modifications to airfoils.
Furthermore, the U.S. Pat. No. 787,503 by General Motors Corporation describes airfoils for high efficiency/high lift fans. This invention concerns airfoils for use for low Reynolds numbers. Compared to airfoil flows with Reynolds numbers above approximately 1,000,000 airfoil flows with Reynolds numbers below approximately 1,000,000 have different flow patterns in which the laminar flows are much more dominant. This means that laminar separation bubbles are much bigger and more or less always a part of the flow pattern. For high Reynolds numbers, i.e. above 1,000,000, laminar separation bubbles are not very dominant except of some airfoils for angles of attack above maximum lift. Thus, airfoils used for Reynolds numbers below 1,000,000 are behaving quite different from airfoils used for Reynolds numbers above 1,000,000. In accordance with this, neither design methods nor modifications have been disclosed.
As the computer power available has been ever increasing and thereby the methods available for simulating the flow past airfoil sections and blades has correspondingly become more sophisticated it is now possible to calculate the flow past two-dimensional- and three dimensional-lifting bodies.
By these new possibilities it is possible to study the flow in higher details and more interesting, as applied in the present invention, it is possible to simulate different flow situations. Also, the increasing computer power has made it possible to optimise complex problems by numerical means. For instance, the combination of flow simulations and numerical optimisations of the airfoil section shape or blade shape has improved the possibility of optimising airfoil sections and blades or parts thereof of existing airfoil sections and blades.
According to the present invention it has been found that an airfoil section or blade or an aerodynamic device used for modification of an airfoil section or a blade may be designed so that the sections or blades does not suffer the same drawbacks as the prior art devices and actually solve or improve the following problems: the risk of double stall, sensitivity to leading edge roughness in stall, low lift-drag ratio just before stall and in stall, big variations of aerodynamic loads in stall and negative aerodynamic damping.
According to the invention, it has been found that airfoil sections or blades wherein the transition point which tricks leading edge stall is to be situated downstream of the free transition point in order to avoid double stall and to decrease the variations of the aerodynamic loads in stall of the blade. The location of the transition point which tricks leading edge stall is at a location where a leading edge laminar separation bursts, i.e. the transition point has moved so much downstream that the flow cannot attach the surface. Also, it has been found that the position of the free transition point, also called natural transition point, the pressure distribution and the shape of the airfoil section or blade can control the overall aerodynamic performance in stall. As will appear from the detailed description herein, this gives rise to a new understanding of the decisive criteria for designing airfoil sections or blades; in particular two- or three-dimensional airfoil sections used for aerodynamically purposes.
In general, the flow produced by airfoil sections or blades designed according to the present invention have the potential to fulfil certain desired characteristics. For instance, if it is desired to avoid the tendency to double stall it is required in the design process that the flow is stable in the sense that if a suction side leading edge laminar separation bubble is present then this bubble is substantially stable in time. As mentioned above this is provided by designing the airfoil sections or blades so that the position of the free transition point is situated upstream of the transition points which tricks leading edge stall, which in turn is assured by numerical modelling the flow past the airfoil or blade.
Thus, the present invention relates in a first aspect to a modified wind turbine airfoil section comprising, such as being constituted by, composed of or made up by, an airfoil section and a contour modification thereto. It has been found according to the present invention that it is essential that the modified airfoil section has a contour modification wherein the first, the second and optionally the third derivative of the outer contour of the contour modification are smooth and continues, such as substantially smooth and continues in order to modify airfoils according to the problems discussed above.
The terms xe2x80x9csmooth and continuosxe2x80x9d is herein used in accordance with the ordinary aerodynamical sense of those terms. Accordingly, xe2x80x9csmooth and continuosxe2x80x9d is used to denote a contourxe2x80x94or surfacexe2x80x94which do not spoil the flow past the contour or surface. Thus, in general the mean contour or mean surface of an airfoil section or blade is at least considered smooth and continuos, preferably quantified by having first, second and optionally third derivatives being smooth and continues, if that mean contour or mean surface has no bumps or edges. Please also consult section xe2x80x9cBrief explanation of certain termsxe2x80x9d.
Furthermore, it has been found that a modified airfoil section according to the present invention preferably has a contour wherein the first, the second and optionally the third derivative of the contour of the modified airfoil section are smooth and continuos, such as substantially smooth and continuos, except at the trailing edge of the airfoilxe2x80x94that is, not only the modification of the airfoil but the whole airfoil must preferably have a contour being smooth and continuesxe2x80x94preferably, except at the trailing edge.
In particular preferred embodiments, connected to modifying airfoils in order to avoid double stall, it may be preferred that the modified airfoil section according to the present invention has a contour wherein the angle between the suction surface and the chord line evaluated substantially 2% chord length behind the leading edge is larger than 32xc2x0, preferably larger than 33xc2x0, such as larger than 34xc2x0, in some situations preferably larger than 35xc2x0, and even preferably larger than 36xc2x0, preferably larger than 37xc2x0, such as larger than 38xc2x0, preferably larger than 39xc2x0, and even most preferably larger than 40xc2x0.
Alternatively or supplementary to the geometrical constraints on the suction side surface in relation to the embodiments pertaining to double stall it may be preferred that the suction side free transition point is located upstream of the transition point which tricks bursting of a leading edge separation bubble. These transition points are preferably evaluated at a Reynolds number between 1,000,000 and 20,000,000, but the actual size of the Reynolds number depends, of course, of the application of the modified airfoil section.
In such situations, the suction side free transition point may preferably be located more than 0.25% chord length, preferably more than 0.5% chord length, such as more than 1% chord length, preferably more than 1.5% chord length, in some situations more than 2% chord length, and even more than 3% chord length, preferably more than 5% chord length, such as more than 7% chord length, preferably more than 8.5% chord length, and even more than 10% chord length upstream of the transition point which tricks bursting of a leading edge separation bubble, preferably being evaluated close to or at maximum lift, such as at angles of attack between 2xc2x0 before and 4xc2x0 after maximum lift. Again, the transition points are preferably evaluated at a Reynolds number between 1,000,000 and 20,000,000 but the actual size of the Reynolds number depends, of course, of the application of the modified airfoil section.
In other preferred embodiments relating to modifying airfoils in order to minimise or avoid the influence of leading edge roughness it may be preferred that the contour of the modified airfoil section according to the present invention preferably is so shaped that the suction side free transition point is located less than 10% chord length, preferably less than 8.5% chord length, such as less than 7% chord length, preferably less than 5% chord length, in some situations less than 3% chord length, and even less than 2% chord length, preferably less than 1.5% chord length, such as less than 1% chord length, preferably less than 0.5% chord length, and even less than 0.25% chord length from the leading edge, preferably being evaluated around or at maximum lift, such as at angles of attack between 6xc2x0 before and 6xc2x0 after maximum lift. The transition points is preferably evaluated at a Reynolds number between 1,000,000 and 20,000,000, but the actual size of the Reynolds number depends, of course, of the actual application of the modified airfoil.
Such preferred embodiments may very advantageously be combined with embodiments pertaining to double stall and the other embodiments discussed below.
According to present invention a high lift-drag ratio is often aimed at either alone or in combination with the measures relating to double stall and/or influence on leading edge roughness. In preferred embodiments of the modified airfoil section according to the present invention the modified airfoil section may preferably have a lift-drag ratio being higher than the airfoil without the contour modification, said lift drag-ratio being preferably evaluated in an interval ranging from 8 degrees angles of attack before stall to maximum lift.
More specifically, it is often preferred that a modified airfoil section according to the present invention has a lift drag ratio being larger than 20, such as larger than 50, preferably larger than 60, such as larger than 75 and most preferably larger than 100, said lift drag-ratio being preferably evaluated in an interval ranging from 5 degrees angles of attack before stall to maximum lift.
Furthermore, preferred embodiments of a modified airfoil section minimising aerodynamic loads alone or in combination with the other embodiments of the modified airfoil section are preferably provided by airfoil sections, wherein the angle between the suction surface and the chord line evaluated substantially 2% chord length behind the leading edge is larger than 32xc2x0, preferably larger than 33xc2x0, such as larger than 34xc2x0, in some situations preferably larger than 35xc2x0, and even preferably larger than 36xc2x0, preferably larger than 37xc2x0, such as larger than 38xc2x0, preferably larger than 39xc2x0, and most preferably larger than 40xc2x0.
In such situations airfoil sections according to the present invention are preferably shaped so that the suction side free transition point is located more than 0.25% chord length, preferably more than 0.5% chord length, such as more than 1% chord length, preferably more than 1.5% chord length, in some situations more than 2% chord length, and even more than 3% chord length, preferably more than 5% chord length, such as more than 7% chord length, preferably more than 8.5% chord length, and even more than 10% chord length upstream of the transition point which would trick bursting of a leading edge separation bubble, preferably evaluated close to or at maximum lift, such as of angles of attack between 2xc2x0 before and 4xc2x0 after maximum lif. The transition points are preferably evaluated at a Reynolds number between 1,000,000 and 20,000,000, but the actual size of the Reynolds number depends, of course, on the actual application of the modified airfoil section.
When the measure to be fulfilled by the modified airfoil is relating to aerodynamic damping alone or in combination with the other measures, embodiments of the modified airfoil are often preferred, wherein normalised minimum edgewise damping, cx, is greater than xe2x88x922, preferably greater than xe2x88x921.8, such as greater than xe2x88x921.6, preferably greater than xe2x88x921.4, in some situations greater than xe2x88x921.2, preferably greater than xe2x88x921.0 and even greater than xe2x88x920.8 and wherein the normalised minimum flapwise damping, cy, is greater than xe2x88x926, preferably greater than xe2x88x925, such as greater than xe2x88x924, preferably greater than xe2x88x923, in some situations greater than xe2x88x922, preferably greater than xe2x88x921 and even greater than 0.
The normalised damping coefficients, cx and cy should preferably be obtained by normalising CX and CY by 0.5*c*p*W, and should preferably be evaluation after maximum lift, such as at angles of attacks from maximum lift to 10xc2x0 after maximum lift. The damping is preferably evaluated at a Reynolds number between 1,000,000 and 20,000,000, but the actual size of the Reynolds depends, of course, on the actual application of the airfoil.
The present invention relates in another aspect to a modified blade for a wind turbine having at least one modified airfoil section according to present invention. Thus, in practical implementations in accordance with the present aspect of the present invention an entire blade has not to be modified but only those parts or that part of a blade which suffers one or more of the problems discussed above. On the other hand, in case the entire blade suffers one or more of the problems discussed above all the airfoil sections of the blade may preferably be modified according to the present invention.
Preferably, a modified blade for a wind turbine having at least one modified airfoil section according to the present invention is modified so that bursting of a leading edge laminar separation bubble is avoided in at least the vicinity of the at least one airfoil section being modified.
Preferably, the modified blade for a wind turbine according to the present invention is a blade wherein the contour modification is provided by an aerodynamic device mounted on a blade.
In very important embodiments of the modified blade for a wind turbine according to present invention the aerodynamic device is shaped so that once mounted on a blade, the surface at least in the vicinity of the intersections between the device and the blade are smooth and continues. This measure is preferably provided by shaping the device at its extremities similar to the shaped of the blade in the regions close to these extremities.
Accordingly, it is often preferred that the aerodynamic device of the modified blade for a wind turbine is shaped so that once mounted on a blade, the tangent to the surfaces in the vicinity of the intersection(s) between the aerodynamic device and the blade is(are) smooth and continuos.
According to the findings of the present invention modifications pertaining to the problems discussed above may preferably be applied mainlyxe2x80x94or onlyxe2x80x94in the leading edge region of the blade. Thus, in preferred embodiments of the present invention the aerodynamic device modifies a blade only in the leading edge region or modifies substantially only the leading edge region of a blade.
In agreement with the different problems solved by the invention, the blade on which the aerodynamic device is mounted may preferably a blade having an inclination towards leading edge laminar separation, such as producing a flow past the airfoil having leading edge laminar separation at a Reynolds number between 1,000,000 and 20,000,000 and preferably at an angle of attack between 5xc2x0 before maximum lift and 8xc2x0 after maximum lift.
Different measures exist in order to implement modifications of blades according to the present invention. In a particular important embodiment, the contour modification or aerodynamic device may preferably be provided by adding material, such as a hardening material, to a blade.
In other equally important embodiments of the implementation of the modification, the modification and/or aerodynamic device may preferably be made as a flexible sheet, such as a rubber sheet and/or plastic sheet, having the form of the modification and/or aerodynamic device.
Alternatively (or in combination) the contour modification or aerodynamic device may preferably be made as a flexible sheet, such as rubber sheet or plastic sheet, being substantially uniform in one direction and the modifications needed in order to modify a blade may preferably be provided by compression and/or extraction of the flexible sheet.
In many cases it is advantageously to prepare the contour modification of site. Thus, the contour modification or aerodynamic device may preferably be made as a prefabricated device to be attached to a blade. Such prefabrication may preferably be obtained by extruding a flexible material such as rubber, plastic or non-plastic material such as glass fibre, aluminium or steel. In such cases the geometry of the device may be some average of the modifications for each of the selected airfoil sections to be modified.
Such a prefabricated technique may also very advantageously be applied in connection with fabrication of new blade, i.e. a blade not yet being in use. When such a new blade is manufactured the leading edge is normally not smooth, which non-smoothness is remedied by cutting away material of the blade in the leading edge region. In connection with the present invention, the whole leading edge region is removed from the blade and replaced by a modification according to the present invention.
In connection to this, it should be noted that the description of the modification according to the present invention has been focused on a positive modification, that is a modification moving the contour of the airfoil section out in the flow. Anyhow, the invention is equally well suited in case of a negative modification, that is a modification moving the contour away from the flow, is required. In this case removal of material from a blade may provide the practical implementation.
The invention relates in another aspect to a method of modifying, by use of a computer system, the shape of a blade or an airfoil section. In the method according to invention a design set-up has been provided in terms of
an objective function to be minimised representing preferably the negative efficiency of the airfoil section or blade, such as representing lift-drag ratios and/or the driving force which is the force in the chord direction in upstream direction at least at one angle of attack,
design variables representing points on at least a part of the airfoil section or of the blade,
geometrical constraint(s) stipulating that each geometrical modification to the airfoil section or to the blade determined by the method must be so that the first the second and optionally the third derivative of the airfoil section contour or blade contour in at least in the vicinity of the intersection between the modification of the airfoil section or the blade and the non-modified part of the airfoil section of the blade are smooth and continuos, such as substantially smooth and continuos,
aerodynamically constraint(s), such as constraints interrelating the distance between the free transition point and the transition point which tricks bursting of a leading edge separation bubble, eventually expressed in term of geometrical constraint(s).
In put to the method are, of course, also fluid dynamical parameters such as Reynolds number, velocity/velocities, viscosity, density, Mach number etc.
The method utilises the set-up and comprises the following steps:
a) providing an initial shape of the airfoil section or blade, preferably being either an existing airfoil, an initial guess on the airfoil to be designed or an airfoil shape enabling a flow to be calculated,
b) simulating such as calculating a number of flows past the airfoil section or blade necessary to evaluate the aerodynamically constraints,
c) and if the aerodynamically constraints is not fulfilled then the initial shape of the airfoil section or blade is modified by modifying the design variables based on minimisation of the objective function and respecting geometrical constraints, thereby providing a new shape of the airfoil section or blade, and repeating steps b) and c) based on the new shape of the airfoil until the objective function is minimised thereby providing a modified airfoil.
In its basic form, the geometrical constraints relate particularly to extremities of modifications determined by or during execution of the method. In preferred embodiments of the method according to the invention the geometrical constraint(s) stipulates or further stipulates that each geometrical modification to the airfoil section or to the blade determined by the method must have smooth and continues, such as substantially smooth and continues first, second and optionally third derivatives. Such preferred embodiments will ensure that a modification determined byxe2x80x94or during execution ofxe2x80x94the method will be smooth and continues.
In a particular preferred embodiment of the method according to the present invention, it is often preferred that the geometrical constraints stipulate or further stipulates that the contour of the modified airfoil section or the contour of the modified blade determined by the method must have smooth and continues, such as substantially smooth and continues, first, second and optionally third derivatives except at the trailing edge.
In preferred embodiments of the method, in connection with double stall, it is often preferred that the aerodynamically constraint(s) stipulates or further stipulates that the free transition point is located upstream of the transition point that tricks bursting of a leading edge separation bubble. In such situations, it may be preferred that the free transition point is to be located more than 0.25% chord length, such as more than 0.5% chord length, preferably more than 1% chord length, such as more than 1.5% chord length, preferably more than 2% chord length of the chord length upstream of the transition point which trick bursting of a leading edge separation bubble, preferably evaluated close to or at maximum lift, such as at angles of attack between 2xc2x0 before and 4xc2x0 after maximum lift.
Alternatively or in combination with the geometrical expressed aerodynamically constraint(s) it is often preferred that the aerodynamically constraint(s) stipulates or further stipulates attached suction side flow.
In yet another preferred embodiment of the method in connection with double stall the aerodynamically constraint(s) may preferably be expressed in terms of geometrical constraint(s) as the angle between the suction surface and the chord line evaluated at substantially 2% chord length behind the leading edge to be larger than 32xc2x0, preferably larger than 33xc2x0, such as larger than 34xc2x0, in some situations preferably larger than 35xc2x0, and even preferably larger than 36xc2x0, preferably larger than 37xc2x0, such as larger than 38xc2x0, preferably larger than 39xc2x0, and most preferably larger than 40xc2x0.
It is often preferred commonly for all the embodiments of the method pertaining to double stall that the objective function stipulates or further stipulates maximisation of the efficiency such as lift-drag-ratio at angles of attack between zero lift and maximum lift, e.g. xe2x88x923xc2x0 to 13xc2x0 angles of attack.
Those preferred embodiments of the method according to present invention discussed above in connection with double stall might very advantageously be combined with embodiments of the method pertaining to other flow problems as discussed below.
Accordingly, in another preferred embodiment, pertaining to leading edge roughness sensitivity, the aerodynamic constraint(s) stipulates or further stipulates that the suction side free transition point, must be located less than 10% chord length, preferably less than 8.5% chord length, such as less than 7% chord length, preferably less than 5% chord length, in some situations less than 3% chord length, and even less than 2% chord length, preferably less than 1.5% chord length, such as less than 1% chord length, preferably less than 0.5% chord length, and even less than 0.25% chord length from the leading edge, preferably being evaluated around or at maximum lift, such as at angles between 6xc2x0 before 6xc2x0 after maximum lift.
In connection with such preferred embodiments or combinations thereof, it is often preferred that the objective function stipulates or further stipulates maximisation of the lift-drag-ratio at or between 2xc2x0 and 10xc2x0 degrees angles of attack. In some situations it may be preferred that maximisation takes place between angles of attack showing zero lift and maximum lift.
In order to achieve high lift-drag ratios in general or in combination with the other measures to be achieved, it is often preferred that the objective function stipulates maximisation of the lift-drag-ratio at or between 8xc2x0 and 12xc2x0 degrees angles of attack. In some situations it may be preferred that the maximisation of the lift-drag-ratio takes place at or between 8xc2x0 angles of attack before maximum lift and the angle of attack showing maximum lift.
In preferred embodiments of the method according to the present invention, in which the measure to be achieved pertains to aerodynamic loads, it is often preferred that the aerodynamically constraint(s) is(are) expressed in terms of geometrical constraint(s) as the angle between the suction surface and the chord line evaluated substantially 2% chord length behind the leading edge must larger than 32xc2x0, preferably larger than 33xc2x0, such as larger than 34xc2x0, in some situations preferably larger than 35xc2x0, and even preferably larger than 36xc2x0, preferably larger than 37xc2x0, such as larger than 38xc2x0, preferably larger than 39xc2x0, and most preferably larger than 40xc2x0.
In combination theretoxe2x80x94or alonexe2x80x94it may be preferred that the aerodynamically constraint(s) stipulates or further stipulates that the free transition point is located downstream of the transition point that tricks bursting of a leading edge separation bubble.
In such situations it may be preferred that the aerodynamically constraint(s) stipulates or further stipulates that the free transition point, is located more than 0.25% chord length, preferably more than 0.5% chord length, such as more than 1% chord length, preferably more than 1.5% chord length, in some situations more than 2% chord length, and even more than 3% chord length, preferably more than 5% chord length, such as more than 7% chord length, preferably more than 8.5% chord length, and even more than 10% chord length upstream of the transition point which would trick bursting of a leading edge separation bubble; preferably evaluated close to or at maximum lift, such as angles of attack between 2xc2x0 before and 4xc2x0 after maximum lift.
In connection with such preferred embodiments or combinations thereof, it is often preferred that the objective function stipulates maximisation of the lift-drag-ratio at or between 2xc2x0 and 10xc2x0 degrees angles of attack, or preferably at or between the angles of attack showing zero lift and maximum lift.
According to preferred embodiments of the method, pertaining to aerodynamic damping, it may be preferred that the aerodynamic constraint(s) stipulates or further stipulates that the normalised minimum edgewise damping, cx, should be greater than xe2x88x922, preferably greater than xe2x88x921.8, such as greater than xe2x88x921.6, preferably greater than xe2x88x921.4, in some situations greater than xe2x88x921.2, preferably greater than xe2x88x921.0 and even greater thanxe2x88x920.8, and wherein the normalised minimum flapwise damping, cy, should be greater than xe2x88x926, preferably greater than xe2x88x925, such as greater than xe2x88x924, preferably greater than xe2x88x923, in some situations greater than xe2x88x922, preferably greater than xe2x88x921 and even greater than 0.
The normalised damping coefficients, cx and cy, should preferably be obtained by dividing CX and CY by 0.5*c*p*W and the normalised damping coefficients, cx and cy, should preferably be evaluated after maximum lift, such as angles at attacks from maximum lift to 10xc2x0 after maximum lift.
In connection theretoxe2x80x94or in combination with the other embodiments mentioned abovexe2x80x94it is often preferred that the objective function stipulates or further stipulates maximisation of the lift-drag-ratio at or between 2xc2x0 and 10xc2x0 degrees angles of attack.
According to the above discussion of the different aspects of the invention and in particular the discussion of different embodiments thereof, it is mentioned that the different embodiments may very advantageously be combined. Combining the different embodiments one might have to decide which embodiments is the most important because some times may be a compromise between different desired characteristics.